Force Units

Newton

The newton, N, is a SI derived unit for measuring force. The newton in SI base units is 1 N =1 kg⋅m⋅s ⁻² which is equivalent to mass over acceleration (m/a) [1].

One newton is the force required to accelerate a one kilogram mass at the rate of one metre per second squared, or change in velocity, in a given direction [1].

[1]

Other examples include: a kilogram of mass exerting an average of 9.8 N due to the gravity, the weight of an average adult exerts a force of about 608 N (608 N = 62 kg × 9.80665 m·s^-2) [1].

It is common to see force expressed in kilonewtons (kN) where 1 kN = 1000 N. For example, 1 kN is the equivalent of about 102 kg under the force of gravity. Another example, a platform rated at 321 kilonewtons will safely support a load of 32,100 kilograms [1].

Pascal

The pascal, Pa, is a SI derived unit of pressure, used to quantify internal pressures, stress, the young's modulus and ultimate tensile strength. The pascal in SI base units is 1 Pa = 1kg·m^-1·s^-2 which is equivalent to one newton per metre square (N/m²) or one joule per metre cubed (J/m³) [2].

In material science, the pascal measures stiffness, tensile strength, and compressive strength of materials. Since the pascal is a very small quantity, the megapascal (MPa) and gigapascal (GPa) are more commonly used. For example, the Young's modulus of aluminium, copper and diamond are 69 GPa, 117 GPa and 1220 GPa respectively [2].

A good way to help visualize and understand pascals is to use a constant force of one newton and varying area. one newton over an area of one metre squared will result in a pressure of one pascal whereas one newton applied to a one millimetre squared area will result in a pressure equal to one megapascal. Now use a constant area of one metre squared with varying force. A force of one thousand newtons over an area of one metre squared would result in one kilopascal which would require, under earths gravitation, a mass of 102 kilograms.

[3]

Newton-second

The newton-second, N·s, is a SI derived unit used for measuring impulse. The newton-second in SI base units is 1 N·s = kg·m·s^-1 which is dimensionally equivalent to momentum, kilogram-metre per second [4].

In classical mechanics, impulse, J or Imp, is the integral of force over the time interval. Impulse, like force, is a vector quantity [5].

Given that impulse is dependent on mass (m) and change in velocity (Δv), different example scenarios can be used to quantify varying sizes of newton-second. For example, if a 420 gram soccer ball starts at rest (v_i = 0) and is then kicked such that its speed is 2.4 m/s (v_f =2.4), then it will experience an impulse of about 1 N·s. This also means that is momentum changed from a momentum of 0 to a momentum of 1 [4]. Another example to quantify newton-seconds would be to look at a momentum example. If a space shuttle, with a mass of about 2.03 gigagram (Gg), has a velocity of 8050 m/s, it will have a momentum of 1.63×10¹⁰ N·s [4].

Newton-metre

The newton-metre  is a SI derived unit for measuring torque or a moment. the newton-metre in SI base units is 1 N·m = 1 kg·m²·s^-2 which is dimensionally equivalent to joules (J) [8].

It is sometimes easy to confuse the newton-metre with a newton times a metre, which is a joule. The difference between a newton-metre and a newton times a metre is that a newton-metre creates a twist or rotation about a point whereas a newton times a metre is a push over a distance. For example, exerting 5 newtons of force on a door that is 1 metre away from the hinge would result in a torque of 5 whereas if an object is pushed through 1 metre with a force of 5 newtons then 1 joule of work was done [9].

An example to help quantify a Nm is to consider a 100 gram object extended outward from a pivot point by 1 metre. This 100 gram object will be exerting about 1 N of force down which will create a torque of about 1 Nm about the pivot point.

References

[1] “Newton (unit),” Wikipedia, 05-Jul-2021. [Online]. Available: https://en.wikipedia.org/wiki/Newton_(unit). [Accessed: 30-Jul-2021].

[2] “Pascal (unit),” Wikipedia, 11-Jul-2021. [Online]. Available: https://en.wikipedia.org/wiki/Pascal_(unit). [Accessed: 30-Jul-2021].

[3] “Pressure,” Wikipedia, 28-Jul-2021. [Online]. Available: https://en.wikipedia.org/wiki/Pressure. [Accessed: 30-Jul-2021].

[4] “Newton-second,” Wikipedia, 12-Jun-2021. [Online]. Available: https://en.wikipedia.org/wiki/Newton-second. [Accessed: 03-Aug-2021].

[5] “Impulse (physics),” Wikipedia, 03-Jul-2021. [Online]. Available: https://en.wikipedia.org/wiki/Impulse_(physics). [Accessed: 03-Aug-2021].

[6] “Top 10 health benefits of soccer,” CoachUp Nation. [Online]. Available: https://www.coachup.com/nation/articles/top-10-health-benefits-of-soccer. [Accessed: 06-Aug-2021].

[7] A. Scimecca and A. Pressman, “SpaceX's historic Crewed rocket launch in photos,” Fortune, 08-Apr-2021. [Online]. Available: https://fortune.com/2020/06/01/spacex-photos-rocket-launch-iss-commercial-spaceflight/. [Accessed: 06-Aug-2021].

[8] “Newton-metre,” Wikipedia, 11-Jun-2021. [Online]. Available: https://en.wikipedia.org/wiki/Newton-metre. [Accessed: 06-Aug-2021].

[9] “Newton meter,” Newton meter - Energy Education. [Online]. Available: https://energyeducation.ca/encyclopedia/Newton_meter. [Accessed: 09-Aug-2021].

Contributors: